Show that the set is convex if and only if its intersection with any line is convex. Show that the convex hull of the $S$ set is the intersection of all convex sets ...

Quasiconvex functions play an important role in several branches of applied mathematics (e.g. mathematical programming, minimax theory, games theory, etc.) and of economic analysis (production theory, ...

American Journal of Mathematics, Vol. 138, No. 2 (April 2016), pp. 499-527 (29 pages) This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded ...

Convex geometry and point set configurations form a pivotal area of research in computational geometry, where the primary focus is the study of convex sets and the intricate arrangements of points in ...

Abstract: A portfolio optimization problem is a convex optimization problem that involves a linear objective function with quadratic constraints. One method for solving portfolio optimization problems ...

We show that the boundary of an n-dimensional closed convex set B ⊂ ℝⁿ, possibly unbounded, is a convex quadric surface if and only if the middle points of every family of parallel chords of B lie in ...

Abstract: Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an ...